version 1.8, 2000/02/28 14:10:27 |
version 1.10, 2001/04/10 11:56:29 |
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%% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.7 2000/01/24 12:32:49 noro Exp $ |
%% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.9 2000/09/12 23:09:18 noro Exp $ |
//&jp \section{ 数, 多項式 の CMO 表現 } |
//&jp \section{ 数, 多項式 の CMO 表現 } |
//&eg \section{ CMOexpressions for numbers and polynomials } |
//&eg \section{ CMOexpressions for numbers and polynomials } |
\label{sec:basic1} |
\label{sec:basic1} |
Line 64 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
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Line 64 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
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\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
& & \mbox{ --- ユニバーサルな ゼロを表す. } \\ |
& & \mbox{ --- ユニバーサルな ゼロを表す. } \\ |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
{\sl byte}\, \mbox{a[m]} ) \\ |
{\sl byte}\, \mbox{a[$|$f$|$]} ) \\ |
&:& \mbox{ --- bignum をあらわす. a[i] についてはあとで説明}\\ |
&:& \mbox{ --- bignum をあらわす. a[i] についてはあとで説明}\\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, {\sl ZZ}\, {\rm a}, {\sl ZZ}\, {\rm b}) \\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, |
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{\sl int32}\, {\rm m}, {\sl byte}\, \mbox{a[1]}, \ldots, {\sl byte}\, \mbox{a[$|$m$|$]}, |
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{\sl int32}\, {\rm n}, {\sl byte}\, \mbox{b[1]}, \ldots, {\sl byte}\, \mbox{b[$|$n$|$]})\\ |
& & \mbox{ --- 有理数 $a/b$ を表す. } \\ |
& & \mbox{ --- 有理数 $a/b$ を表す. } \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
& & \mbox{ --- $a/b$ を表す. } \\ |
& & \mbox{ --- $a/b$ を表す. } \\ |
Line 84 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
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Line 86 ZZ, QQ, Zero, Rational, Indeterminate,$\in$ CMObject/B |
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\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
\mbox{Zero} &:& ({\tt CMO\_ZERO}) \\ |
& & \mbox{ --- Universal zero } \\ |
& & \mbox{ --- Universal zero } \\ |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
\mbox{ZZ} &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots |
{\sl byte}\, \mbox{a[m]} ) \\ |
{\sl byte}\, \mbox{a[$|$m$|$]} ) \\ |
&:& \mbox{ --- bignum. The meaning of a[i] will be explained later.}\\ |
&:& \mbox{ --- bignum. The meaning of a[i] will be explained later.}\\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, {\sl ZZ}\, {\rm a}, {\sl ZZ}\, {\rm b}) \\ |
\mbox{QQ} &:& ({\tt CMO\_QQ}, |
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{\sl int32}\, {\rm m}, {\sl byte}\, \mbox{a[1]}, \ldots, {\sl byte}\, \mbox{a[$|$m$|$]}, |
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{\sl int32}\, {\rm n}, {\sl byte}\, \mbox{b[1]}, \ldots, {\sl byte}\, \mbox{b[$|$n$|$]})\\ |
& & \mbox{ --- Rational number $a/b$. } \\ |
& & \mbox{ --- Rational number $a/b$. } \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
\mbox{Rational} &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\ |
& & \mbox{ --- Rational expression $a/b$. } \\ |
& & \mbox{ --- Rational expression $a/b$. } \\ |
Line 219 It is the same as the Lambda expression in Lisp. |
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Line 223 It is the same as the Lambda expression in Lisp. |
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) |
) |
) |
) |
\end{verbatim} |
\end{verbatim} |
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//&jp Leave の成分には, 多項式を含む任意のオブジェクトがきてよい. |
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//&eg Elements of the leave may be any objects including polynomials. |
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\noindent |
\noindent |
Example: |
Example: |
Line 551 $\in$ CMObject/RecursivePolynomial \\ |
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Line 557 $\in$ CMObject/RecursivePolynomial \\ |
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\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{RringDefinition} |
\mbox{RringDefinition} |
& : & \mbox{ {\sl List} v } \\ |
& : & \mbox{ {\sl List} v } \\ |
& & \quad \mbox{ --- v は, 変数名(indeterminate) のリスト. } \\ |
& & \quad \mbox{ --- v は, 変数名(indeterminate) または Tree のリスト. } \\ |
& & \quad \mbox{ --- 順序の高い順. } \\ |
& & \quad \mbox{ --- 順序の高い順. } \\ |
\end{eqnarray*} |
\end{eqnarray*} |
*/ |
*/ |
Line 581 $\in$ CMObject/RecursivePolynomial \\ |
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Line 587 $\in$ CMObject/RecursivePolynomial \\ |
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\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{ Polynomial in 1 variable}\, | \, \mbox{Coefficient} \\ |
\mbox{RringDefinition} |
\mbox{RringDefinition} |
& : & \mbox{ {\sl List} v } \\ |
& : & \mbox{ {\sl List} v } \\ |
& & \quad \mbox{ --- v is a list of names of indeterminates. } \\ |
& & \quad \mbox{ --- v is a list of names of indeterminates or trees. } \\ |
& & \quad \mbox{ --- It is sorted in the decreasing order. } \\ |
& & \quad \mbox{ --- It is sorted in the decreasing order. } \\ |
\end{eqnarray*} |
\end{eqnarray*} |
*/ |
*/ |